Theorem mulcomi 8184

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8160	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 426	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1397   e. wcel 2202  (class class class)co 6017   CCcc 8029   x. cmul 8036

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8132

This theorem is referenced by:  mulcomli  8185  8th4div3  9362  numma2c  9655  nummul2c  9659  9t11e99  9739  binom2i  10909  fac3  10993  tanval2ap  12273  pockthi  12930  decsplit1  13000  decsplit  13001  sincosq4sgn  15552  2logb9irrALT  15697  2lgsoddprmlem2  15834  2lgsoddprmlem3d  15838